1. Field of the Invention
The invention relates to a gain calibration device and method for differential push-pull (hereinafter referred to as DPP) tracking error signals in an optical storage system, and more specifically to a calibration device and method for calibrating the sub beam in the DPP signal component with respect to the synthesized gain (hereinafter referred to as SPPG) of the main beam.
2. Description of the Related Art
FIG. 1 shows the configuration of laser spots on optical discs for the DPP-based tracking error synthesis. As shown in FIG. 1, in the general DPP-based tracking error synthesis, there are three laser beams, including a main beam 12, a first sub beam 13, and a second sub beam 14, projected on the optical disc. Therefore, the DPP tracking error signal TE may be represented as the differential synthesis of the push-pull signal MPP of the main beam 12 and the push-pull signals SPP of the sub beams 13 and 14, as shown in Equation (1):TE=MPP−α·SPP  (1)                wherein  is the synthesized gain SPPG of the push-pull signals SPP of the sub beams 13 and 14 with respect to the push-pull signal MPP of the main beam 12.        
According to the arranged configuration of laser spots on the optical disc as shown in FIG. 1, the push-pull signal MPP of the main beam 12 and the push-pull signals SPP of the sub beams 13 and 14 can be represented as Equations (2) and (3):
                              M          ⁢                                          ⁢          P          ⁢                                          ⁢          P                =                                            A              m                        ·                          sin              ⁡                              (                                                      2                    ⁢                    π                    ⁢                                                                                  ⁢                    x                                    P                                )                                              +                                    A              m                        ·                          K              ⁡                              (                                  t                  ⁢                                                                          ⁢                  i                  ⁢                                                                          ⁢                  l                  ⁢                                                                          ⁢                  t                                )                                              +                      C            m                                              (        2        )                                                                                    S                ⁢                                                                  ⁢                P                ⁢                                                                  ⁢                P                            =                            ⁢                                                S                  ⁢                                                                          ⁢                  P                  ⁢                                                                          ⁢                  P1                                +                                  S                  ⁢                                                                          ⁢                  P                  ⁢                                                                          ⁢                  P2                                                                                                        =                            ⁢                                                [                                                                                    A                        S1                                            ·                                              sin                        ⁡                                                  (                                                                                    2                              ⁢                                                              π                                ⁢                                                                                                                                  ·                                                                  (                                                                      x                                    -                                                                          Q                                      1                                                                                                        )                                                                                                                      P                                                    )                                                                                      +                                                                  A                        S1                                            ·                                              K                        ⁡                                                  (                                                      t                            ⁢                                                                                                                  ⁢                            i                            ⁢                                                                                                                  ⁢                            l                            ⁢                                                                                                                  ⁢                            t                                                    )                                                                                      +                                          C                      S1                                                        ]                                +                                                                                                      ⁢                              [                                                                            A                      S2                                        ·                                          sin                      ⁡                                              (                                                                              2                            ⁢                                                          π                              ⁢                                                                                                                          ·                                                              (                                                                  x                                  +                                                                      Q                                    2                                                                                                  )                                                                                                              P                                                )                                                                              +                                                            A                      S2                                        ·                                          K                      ⁡                                              (                                                  t                          ⁢                                                                                                          ⁢                          i                          ⁢                                                                                                          ⁢                          l                          ⁢                                                                                                          ⁢                          t                                                )                                                                              +                                      C                    S2                                                  ]                                                                                        =                            ⁢                                                                    (                                                                                            A                          S1                                                ·                                                  cos                          ⁡                                                      (                                                                                          2                                ⁢                                π                                ⁢                                                                                                                                  ⁢                                                                  Q                                  1                                                                                            P                                                        )                                                                                              +                                                                        A                          S2                                                ·                                                  cos                          ⁡                                                      (                                                                                          2                                ⁢                                π                                ⁢                                                                                                                                  ⁢                                                                  Q                                  2                                                                                            P                                                        )                                                                                                                )                                    ·                                      sin                    ⁡                                          (                                                                        2                          ⁢                          π                          ⁢                                                                                                          ⁢                          x                                                P                                            )                                                                      +                                                                                                       ⁢                                                                    (                                                                                            A                          S2                                                ·                                                  sin                          ⁡                                                      (                                                                                          2                                ⁢                                π                                ⁢                                                                                                                                  ⁢                                                                  Q                                  2                                                                                            P                                                        )                                                                                              -                                                                        A                          S1                                                ·                                                  sin                          ⁡                                                      (                                                                                          2                                ⁢                                π                                ⁢                                                                                                                                  ⁢                                                                  Q                                  1                                                                                            P                                                        )                                                                                                                )                                    ·                                      cos                    ⁡                                          (                                                                        2                          ⁢                          π                          ⁢                                                                                                          ⁢                          x                                                P                                            )                                                                      +                                                                                                       ⁢                                                                    (                                                                  A                        S1                                            +                                              A                        S2                                                              )                                    ·                                      K                    ⁡                                          (                                              t                        ⁢                                                                                                  ⁢                        i                        ⁢                                                                                                  ⁢                        l                        ⁢                                                                                                  ⁢                        t                                            )                                                                      +                                  (                                                            C                      S1                                        +                                          C                      S2                                                        )                                                                                        (        3        )            wherein symbol x is the offset from the spot center 15 of the main beam 12 to the center 10 of the groove, and is a function of time t. Items related to x are the so-called AC components having higher frequency content than the tilt and affected by the disc runout. Symbols Q1 and Q2 are the distances between the spot centers 16 and 17 of the first and second sub beams 13 and 14 to the spot center 15 of the main beam 12, respectively. Symbol P is the data track pitch (i.e., the distance between the groove centers 10 and 10′) on the optical disc. Symbols Am, As1, and As2 are the AC amplitudes of the tracking error signal TE, and are also the amplitudes of the runout. Symbols Cm, Cs1, Cs2 are the circuit signal offsets (OFFSET) of the OP amplifiers of the front-stage amplifier (RFIC) and the optical signal amplifier (PDIC). K(tilt) is a variable directly proportional to the tilt of the pick-up head, and the tilt of the pick-up head is caused by the lens-shift or the optical mechanism error.
Therefore, substituting Equations (2) and (3) into Equation (1), the tracking error signal TE is represented as Equation (4):
                                                                        T                ⁢                                                                  ⁢                E                            =                            ⁢                                                M                  ⁢                                                                          ⁢                  P                  ⁢                                                                          ⁢                  P                                -                                                      α                    ·                    S                                    ⁢                                                                          ⁢                  P                  ⁢                                                                          ⁢                  P                                                                                                        =                            ⁢                                                (                                                            A                      m                                        -                                          α                      ·                                              (                                                                                                            A                              S1                                                        ·                                                          cos                              ⁡                                                              (                                                                                                      2                                    ⁢                                    π                                    ⁢                                                                                                                                                  ⁢                                                                          Q                                      1                                                                                                        P                                                                )                                                                                                              +                                                                                    A                              S2                                                        ·                                                          cos                              ⁡                                                              (                                                                                                      2                                    ⁢                                    π                                    ⁢                                                                                                                                                  ⁢                                                                          Q                                      2                                                                                                        P                                                                )                                                                                                                                    )                                                                              )                                ·                                                                                                      ⁢                                                sin                  ⁡                                      (                                                                  2                        ⁢                        π                        ⁢                                                                                                  ⁢                        x                                            P                                        )                                                  -                                  α                  ·                                      (                                                                                            A                          S2                                                ·                                                  sin                          ⁡                                                      (                                                                                          2                                ⁢                                π                                ⁢                                                                                                                                  ⁢                                                                  Q                                  2                                                                                            P                                                        )                                                                                              -                                                                        A                          S1                                                ·                                                  sin                          ⁡                                                      (                                                                                          2                                ⁢                                π                                ⁢                                                                                                                                  ⁢                                                                  Q                                  1                                                                                            P                                                        )                                                                                                                )                                    ·                                                                                                                      ⁢                                                cos                  ⁢                                      (                                                                  2                        ⁢                        π                        ⁢                                                                                                  ⁢                        x                                            P                                        )                                                  +                                                      (                                                                  A                        m                                            -                                              α                        ·                                                  (                                                                                    A                              S1                                                        +                                                          A                              S2                                                                                )                                                                                      )                                    ·                                      K                    ⁡                                          (                                              t                        ⁢                                                                                                  ⁢                        i                        ⁢                                                                                                  ⁢                        l                        ⁢                                                                                                  ⁢                        t                                            )                                                                      +                                  (                                                            C                      m                                        -                                                                                                                                        ⁢                              α                ·                                  (                                                            C                      S1                                        +                                          C                      S2                                                        )                                            )                                                          (        4        )            
In order to prevent the tracking error signal TE from being influenced by the variable of K(tilt), a proper value of the synthesized gain SPPG is generally set to make the third item in Equation (4) equal to 0. In the conventional method, it is assumed that:
1. As1=As2=As;
2. Q1=Q2=Q; and
3. Q/P is known.
Substituting the assumed values into Equation (4), the Equation (4) is simplified as Equation (5):
                                                                        T                ⁢                                                                  ⁢                E                            =                            ⁢                                                M                  ⁢                                                                          ⁢                  P                  ⁢                                                                          ⁢                  P                                -                                                      α                    ·                    S                                    ⁢                                                                          ⁢                  P                  ⁢                                                                          ⁢                  P                                                                                                        =                            ⁢                                                                    (                                                                  A                        m                                            -                                              α                        ·                        2                        ·                                                  A                          S                                                ·                                                  cos                          ⁡                                                      (                                                                                          2                                ⁢                                π                                ⁢                                                                                                                                  ⁢                                Q                                                            P                                                        )                                                                                                                )                                    ·                                      sin                    ⁡                                          (                                                                        2                          ⁢                          π                          ⁢                                                                                                          ⁢                          x                                                P                                            )                                                                      +                                                      (                                                                  A                        m                                            -                                              α                        ·                        2                        ·                                                  A                          S                                                                                      )                                    ·                                                                                                                      ⁢                                                K                  ⁢                                      (                                          t                      ⁢                                                                                          ⁢                      i                      ⁢                                                                                          ⁢                      l                      ⁢                                                                                          ⁢                      t                                        )                                                  +                                  (                                                            C                      m                                        -                                          α                      ·                                              (                                                                              C                            S1                                                    +                                                      C                            S2                                                                          )                                                                              )                                                                                        (        5        )            
Therefore, the AC items of the push-pull signals MPP and SPP of the main beam 12 and the sub beams 13 and 14 can be used to calibrate the  value. The calibration method is described as follows:
Step 1: tune the circuit's OFFSET values of Cm, Cs1 and Cs2 to be 0;
Step 2: measure the amplitude of the AC item of the MPP, i.e., MA=Am;
Step 3: measure the amplitude of the AC item of the SPP, i.e.,
            S      ⁢                          ⁢      A        =                  2        ·                  A          s                    ⁢              cos        ⁡                  (                                    2              ⁢              π              ⁢                                                          ⁢              Q                        P                    )                      ;
Step 4: define the synthesized gain of SPP, i.e.,
      α    =                            M          ⁢                                          ⁢                      A            ·                          cos              ⁡                              (                                                      2                    ⁢                    π                    ⁢                                                                                  ⁢                    Q                                    P                                )                                                              S          ⁢                                          ⁢          A                    =                        A          m                          2          ·                      A            S                                ;
Step 5: substitute the  value obtained from Step 4 into Equation (5), and then, a function only containing AC items is obtained as shown in Equation (6):
                                                                        T                ⁢                                                                  ⁢                E                            =                            ⁢                                                M                  ⁢                                                                          ⁢                  P                  ⁢                                                                          ⁢                  P                                -                                                      α                    ·                    S                                    ⁢                                                                          ⁢                  P                  ⁢                                                                          ⁢                  P                                                                                                        =                            ⁢                                                                    (                                                                  A                        m                                            -                                              α                        ·                        2                        ·                                                  A                          S                                                ·                                                  cos                          ⁡                                                      (                                                                                          2                                ⁢                                π                                ⁢                                                                                                                                  ⁢                                Q                                                            P                                                        )                                                                                                                )                                    ·                                      sin                    ⁡                                          (                                                                        2                          ⁢                          π                          ⁢                                                                                                          ⁢                          x                                                P                                            )                                                                      +                                                      (                                                                  A                        m                                            -                                              α                        ·                        2                        ·                                                  A                          S                                                                                      )                                    ·                                                                                                                      ⁢                                                K                  ⁢                                      (                                          t                      ⁢                                                                                          ⁢                      i                      ⁢                                                                                          ⁢                      l                      ⁢                                                                                          ⁢                      t                                        )                                                  +                                  (                                                            C                      m                                        -                                          α                      ·                                              (                                                                              C                            S1                                                    +                                                      C                            S2                                                                          )                                                                              )                                                                                                        =                            ⁢                                                A                  m                                ·                                  (                                      1                    -                                          cos                      ⁢                                              (                                                                              2                            ⁢                            π                            ⁢                                                                                                                  ⁢                            Q                                                    P                                                )                                                                              )                                ·                                  sin                  ⁡                                      (                                                                  2                        ⁢                        π                        ⁢                                                                                                  ⁢                        x                                            P                                        )                                                                                                          (        6        )            
It should be noted that the conventional method has to satisfy three assumptions. However, the values of Q/P, As1, As2, Q1, Q2 vary with different pick-up heads and optical discs. Therefore, the information cannot be obtained during the duration for correcting the SPP gain. Accordingly, the correct gain  for SPP cannot be obtained using the conventional method.